This early I would be selective of when and where you are shooting an animal. Shooting an elk in the open in the morning a few miles from a road is not going to give you a very good chance of getting that meat cooled off. An elk's body temperature is over 100 degrees, so you'd be surprised even on a 90 degree day how quickly that meat can start cooling off if you can get it hung in some good shade. It will also keep, better than most think it will, in the shade, if it is hung up where it won't see the sun during the day.
I'd also say evenings are better. If you are doing all the hard work solo, then an elk takes time to process and pack. Even if you shoot one at first light in the morning, there is no way you are getting that whole thing processed and packed out before the hot part of the day. On the other hand, from late afternoon on the temperatures are only going to drop so time only helps instead of hinders what you are trying to do. I'd even do some packing at night to help avoid transporting the meat during the heat of the day.
The best eating elk I have ever had was killed August 31st on a 90+ degree day in the early evening. We got that bull processed as quick as possible and hanging bone in. In just 30 minutes in the shade, the meat was already getting cool to the touch. I thankfully had a few people to help pack meat out and we got it all packed out of there that night getting back to camp around 3 in the morning. Didn't have any meat loss and like I said it ended up being the best elk meat I've ever had. Early season animals have been feeding on all the best stuff, so if you can figure out how to take care of the meat, in my opinion, they are some of the best eating. Good luck on your hunt!